Answer
$x=\dfrac{1}{8}$
Work Step by Step
$\log_{5}(x+3)-\log_{5}x=2$
Combine $\log_{5}(x+3)-\log_{5}x$ as the $\log$ of a division:
$\log_{5}\dfrac{x+3}{x}=2$
Rewrite in exponential form:
$5^{2}=\dfrac{x+3}{x}$
$\dfrac{x+3}{x}=25$
Take $x$ to multiply the right side of the equation:
$x+3=25x$
Solve for $x$:
$x-25x=-3$
$-24x=-3$
$x=\dfrac{-3}{-24}$
$x=\dfrac{1}{8}$
